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A Unified Curvature Definition for Regular, Polygonal, and Digital Planar Curves

Authors
  • Liu, Hairong1, 2
  • Latecki, Longin Jan3
  • Liu, Wenyu1
  • 1 HuaZhong University of Science and Technology, Luoyu Road, No. 1037, Wuhan, Hubei, 430074, China , Wuhan (China)
  • 2 Microsoft Research Asia, Beijing, 100080, China , Beijing (China)
  • 3 Temple University, Philadelphia, PA, 19122, USA , Philadelphia (United States)
Type
Published Article
Journal
International Journal of Computer Vision
Publisher
Springer-Verlag
Publication Date
Mar 29, 2008
Volume
80
Issue
1
Pages
104–124
Identifiers
DOI: 10.1007/s11263-008-0131-y
Source
Springer Nature
Keywords
License
Yellow

Abstract

In this paper, we propose a new definition of curvature, called visual curvature. It is based on statistics of the extreme points of the height functions computed over all directions. By gradually ignoring relatively small heights, a multi-scale curvature is obtained. The theoretical properties and the experiments presented demonstrate that multi-scale visual curvature is stable, even in the presence of significant noise. To our best knowledge, the proposed definition of visual curvature is the first ever that applies to regular curves as defined in differential geometry as well as to turn angles of polygonal curves. Moreover, it yields stable curvature estimates of curves in digital images even under sever distortions. We also show a relation between multi-scale visual curvature and convexity of simple closed curves.

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